Molecular Mechanics Study of Potential Energy Surface of Watson-Crick Guanine-Cytosine Base Pair

EDUARDO GONZÁLEZ, ALEXANDRA DERIABINA, VALERY POLTEV

Facultad de Ciencias Físico Matemáticas

Benemérita Universidad Autónoma de Puebla

Apdo. Postal 1152, 72000 Puebla, Puebla

MÉXICO

Abstract:- Molecular mechanics calculations of energy of interaction between Guanine and Cytosine DNA bases were performed for various mutual base positions. It allows to construct a part of detailed potential energy surface of this pair corresponding to Watson-Crick arrangement. Analysis of this surface demonstrated a possibility of substantial consistent variations of mutual base arrangements followed by rather small energy changes. Variations of propeller twist and buckle angles up to 15o are followed by less than 1 kcal/mol changes of interaction energy. Substantial consistent displacements (up to 1A) of one base with respect to another are possible as well.

Key-Words: - Molecular Mechanics, Intermolecular Interactions, Watson-Crick Pairing, Potential Energy Surface

1 Introduction

The computer simulation is a powerful tool for investigation of molecular mechanisms of biological processes. The most important of them are the processes related to the storage, replication, repair and expression of nucleic acids as a genetic material. The sequence of four nucleic acid bases, namely, two purines, adenine (Ade) and guanine (Gua), and two pyrimidines, thymine (Thy) and cytosine (Cyt) in DNA chain contains all the information necessary for cell life. Interactions between the bases and the bases with other parts of the molecular machinery of the cell determine all the genetic processes. Construction of atomic level models of nucleic acids and their complexes is important for understanding physical mechanisms of these processes. Various mutual positions of nucleic acid bases are involved in biological functioning ofnucleicacids. It is difficult to obtain quantitative information about base interactions by experimental methods. In the most of cases these interactions are only a part of interactions in complex systems. All such data refer to a limited set of base positions corresponding to energy minima of the systems considered. The mutual position of bases alternates during nucleic acid functioning. To understand molecular mechanisms of genetic processes in details it is necessary to evaluate energy changes resulting from base rearrangement. It is possible with theoretical and computational methods. Thousands of theoretical works are devoted to computations of the energy of interactions between nucleic acid bases (see e.g. [1-4] and references herein). Methods widely used for such calculations are the methods of molecular mechanics. These methods include computation of interaction energy using rather simple formulas of classical physics with adjustable coefficients (potential functions) and searching for minima of the energy using minimization techniques.

2Problem formulation

As a part of detailed computational study of interactions between nucleic acid bases we are considering various mutual positions of Gua and Cyt bases. The potential energy surface corresponding to vicinity of Watson-Crick Gua:Cyt pair is constructing, and possible variations of nearly planar base pair are estimating.

3Problem Solution

3.1 Method of Calculation. Atom-atom Potential Functions for Calculation of Intermolecular Interactions.

The energy of interactions between Gua and Cyt is calculated as a sum of twin interactions of all atoms constituting the molecules. Each atom-atom interaction consists of Coulomb term and Lennard-Jones 6-12 term, commonly used in molecular mechanics calculations (Equation 1). For description of interaction of hydrogen atoms capable to form H bonds, 6-12 term is substituted by 10-12 term (Equation 2).

Eij=eiej/rij-Aij/rij6+Bij/rij12 (1)

Eij=eiej/rij-Aij(10)/rij10+Bij(10)/rij12 (2)

In these equations rij is the distance between atoms i and j, ei and ej are charges on atoms i and j. The coefficients Aij(10), Bij(10), Aij and Bij are adjustable parameters, which were changed recently to reproduce more precisely experimental values of interaction energy in base pairs and average inter atomic distances in H bonds [4].

1-methylcytosine and 9-methylguanine are considered to simulate better the parts of nucleic acid chains. The energy is calculated and minimized as a function of 6 variables, corresponding to the displacement of one base with respect to another along x, y and z axes, and to rotation around these axes. Standard minimization techniques are used. Some variables were fixed at sets of values to study potential energy surface.

3.2Minima of Energy of Interaction between Gua and Cyt.

Like for any pair combinations of bases, there are three types of mutual Gua and Cyt arrangements in local energy minima. One type corresponds to nearly planar positions of bases and formation of intermolecular H bonds. Watson-Crick pairs Ade:Thy and Gua:Cyt (Fig. 1) are minima of this type.

Fig. 1. Watson-Crick Gua:Cyt pair with three H bonds (shown by dotted lines). 9-methylguanine and 1-methylcytosine are displayed as used in all the computations.

The second type refers to nearly parallel arrangement of bases one above another (base stacking), and the last type corresponds to substantially non-planar or nearly perpendicular molecule positions. As Gua and Cyt are more polar molecules than Ade and Thy, their electrostatic interactions are stronger, Watson-Crick pair Gua:Cyt is the deepest minimum of all possible pairwise base interactions. This base combination has less number of minima of the second and third type than other combinations, and the energy in these minima are twice or more less negative than in the global one. As a result, the minimization starting from the most of mutual base positions leads to Watson-Crick pair.

3.3Gua-Cyt interactions in vicinity of Watson-Crick pair.

Thus, we concentrate ourselves on detailed study of a part of potential energy surface, corresponding to vicinity of Watson-Crick pair. We performed calculations of energy at changing each of six variables when all other ones are fixed at positions corresponding to the energy minimum, at changing one variable when others are free, and fixing two variables at a set of positions while four others are free. Some of the results obtained are rather evident, e.g. a possibility to make H bonds somewhat longer without drastic energy changes, while it is impossible to shorten H bonds without energy increase. It is possible to distort H bond linearity and pair planarity for several degrees. Some other results were not evident without computations. Two examples of results obtained are displayed in Figures 2 and 3. It appears, that variations of propeller twist of the pair (rotation of one base in respect to another about long axis of pair, horizontal direction in Fig. 1) and pair buckle (rotation around perpendicular axes) are possible for several degrees without substantial energy changes even under fixing all the other variables (Figs. 2 and 3). Much more pronounced consistent variations of pair parameters (i.e. changing of one or two variables and minimization in respect to others) are possible. There exist such directions in six-dimensional space of variables, which correspond to minor changes of energy (not more, than energy of thermal fluctuations) under substantial variable changes (up to 20o for propeller twist and buckle, up to 1A for displacement along coordinate axes). Rather small variable changes in other directions (e.g. corresponding to mutual base displacements in the plane of the pair) result in substantial energy increase. Using these results, it is possible to understand an experimental fact, that practically all base pairs of all the oligonucleotide duplexes studied are not planar (see e.g. [5, 6] and references herein). Interactions between bases in the pair cannot prevent substantial planarity distortions provoked by interactions with neighbor pairs. Variations of propeller twist are frequently more pronounced as compared to buckle variations.

Fig.2. Dependence of the energy of interaction between Gua and Cyt (E) on propeller twist (TW). All other parameters are fixed in the positions of global energy minimum.

Fig. 3. Dependence of the energy of interaction between Gua and Cyt (E) on the pair buckle (BL). All other parameters are fixed in the positions of global energy minimum.

4 Conclusion

Potential energy surface of interaction between Gua and Cyt bases of DNA has some specific features as compared to that of other pair combinations of bases. The global energy minimum of Gua-Cyt interactions, corresponding to nearly planar Watson-Crick pair with three H bonds, is the deepest minimum from all possible minima for base pairs. As this minimum is of twice or more negative value as compared to nearly all other Gua-Cyt minima, energy minimization from the most of mutual base positions leads to this minimum. Rather great consistent mutual base displacements (up to 1A) and rotations (up to 15o) do not change interaction energy by more than 1 kcal/mol. This result explains rather different pair geometry in nucleic acid oligomer duplexes.

Acknowledgements

This work is partially supported by the CONACyT, Mexico, grant No.41885-E

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